Electric Drift Velocity Research Articles

Two-term Boltzmann approximation versus Monte-Carlo simulation: effect of magnetic field

In this paper, we investigate the spatial-local electron energy distribution function (eEDF) interacting with a background gas at the sub-atmospheric pressure in a wide range of applied crossed electric and magnetic fields using the Boltzmann kinetic equation. We compare solutions obtained using two numerical approaches (deterministic two-term approximation and stochastic Monte Carlo method) to identify their applicability in the context of determining drift velocity and reaction constants for electrons. For argon and helium, the upper limit of the reduced electric field applicability of the two-term approximation is discussed. It has been shown that the presence of a magnetic field can reduce this limit. Two explanations are given, one is based on the math of two-term formalism, and the other is based on velocity-space analysis. Two-term approximation fails due to it’s inability to resolve underlying cyclotron oscillation (it should result in an energy variation along the electron’s trajectory). The absence of this feature causes an incorrect estimation of momentum-transfer rate. This results an inaccuracy in the estimation of the angle between electric field and drift velocity.

A numerical solver for investigating the space charge effect on theelectric field in liquid argon time projection chambers

This paper reports the development of a numerical solver aimed to simulate the interaction between the space charge (i.e. ions) distribution and the electric field in liquid argon time projection chamber (LArTPC) detectors. The ion transport equation is solved by a time-accurate, cell-centered finite volume method and the electric potential equation by a continuous finite element method. The electric potential equation updates the electric field which provides the drift velocity to the ion transport equation. The ion transport equation updates the space charge density distribution which appears as the source term in the electric potential equation. The interaction between the space charge distribution and the electric field is numerically simulated within each physical time step. The convective velocity in the ion transport equation can include the background flow velocity in addition to the electric drift velocity. The numerical solver has been parallelized using the Message Passing Interface (MPI) library. Numerical tests show and verify the capability and accuracy of the current numerical solver. It is planned that the developed numerical solver, together with a Computational Fluid Dynamics (CFD) package which provides the flow velocity field, can be used to investigate the space charge effect on the electric field in large-scale particle detectors.

EXPERIMENTAL STUDY OF CURRENT-SHEET-LIKE STRUCTURE IN PINCHING PLASMA FLOW WITH ELECTRIC AND MAGNETIC PROBES

The formation of the current-sheet-like structure under the influence of the external magnetic field in pinching plasma flows generated by the magnetoplasma compressor has been studied. A set of magnetic and electric probes were used to measure the self-generated magnetic field, electron temperature, and electric field locally with sufficiently high temporal and spatial resolution. The data obtained from the probe measurements were used to plot the spatial distributions of electric current and drift velocity in the plasma stream to identify the patterns of plasma flow. In the presence of external magnetic field, the current density, electron temperature, and the ion saturation current reach a peak in close proximity to the sheet. Measurements indicate the outflow of two electron jets of different temperatures from the layer.

Effects of the electric field on soot formation in combustion: A coupled charged particle PBE-CFD framework

In this article, a coupled PBE-CFD framework has been proposed to study counterflow non-premixed flames and soot formation under an external electric field. This framework integrates the population balance equation (PBE) for nanoparticle dynamics into an in-house CFD solver for the multicomponent reactive flows. Different electric properties have been considered in this model. An ion mechanism used in both fuel-rich and fuel-lean combustion is combined with a detailed chemistry for neutral gaseous species and small-size aromatics to retain the full chemistry. In order to model soot particles carrying charges and the movement of the reacting fluid medium in the electric field, a second PBE for the production and transport of charges on soot particles is introduced for the first time and incorporated into the original PBE for the number density of particles. Also, the electric force for the gas mixture is included in the momentum equations. The electric drift velocities for ions and soot particles are also considered in the transport equations of ions and the PBE of soot particles, respectively. The simulations have shown that the presence of the electric field modifies the stagnation plane of the counterflow flames and reduces the soot formation in both rich-fuel and lean-fuel conditions in agreement with experimental observations. The application of the soot particle charging model, accompanied by a proper electric correction factor on the nanoparticle processes of nucleation and surface growth, significantly improves the stability of the flame structure. The introduction of the electric correction factor reveals that the suppression of soot formation in an electric field is mainly caused by the inhibited chemical reactions of the PAH nucleation and particle surface growth, which is more important than the electric drift of the charged particles. Reducing the critical size of the particle charging process enhances the electric drift of nascent soot, thus lessening its subsequent evolution.

Rotation and shear control of a weakly magnetized plasma column using current injection by emissive electrodes

The evolution of the radial profile of the rotation of a weakly magnetized plasma column is investigated experimentally in a radio-frequency argon plasma at low pressure when a strong electron current is emitted by large emissive cathodes. Current injection from large emissive cathodes over a background plasma column (with a plasma density of a few $10^{18}\ \textrm {m}^{-3}$ ) is characterized. Radial scans of the ion velocity show that a continuous control of the rotation profile may be obtained using two spatial configurations for the locations of the emissive cathodes (either in the centre or at the edge of the plasma column). The rotation profile results from the electric drift velocity, damped by the drag exerted on the ions. We demonstrate that the evolution of the rotation profile with the injected current is then controlled by the modification of the plasma potential profile in the presence of strongly emissive cathodes.

Key impact of phase dynamics and diamagnetic drive on Reynolds stress in magnetic fusion plasmas

Reynolds stress is a key facet of turbulence self-organization. In the magnetized plasmas of controlled fusion devices, the zonal flows that are driven by the averaged Reynolds stress modify the confinement performance. We address this problem with full-f gyrokinetic simulations of ion temperature gradient-driven turbulence. From the detailed analysis of the three-dimensional electric potential and transverse pressure fields, we show that the diamagnetic contribution to the Reynolds stress—stemming from finite Larmor radius effects—exceeds the electrostatic contribution by a factor of about two. Both contributions are in phase, indicating that pressure does not behave as a passive scalar. In addition, the Reynolds stress induced by the electric drift velocity is found to be mainly governed by the gradient of the phase of the electric potential modes rather than by their magnitude. By decoupling Reynolds stress drive and turbulence intensity, this property indicates that a careful analysis of phase dynamics is crucial in the interpretation of experiments and simulations.

Drift Motion of Charged Particles in Inhomogeneous Magnetic and Strong Electric Fields

Distinctive features of the drift motion of a nonrelativistic charged particle in slowly varying magnetic and strong electric fields, for which the assumption that the electric drift velocity is small as compared to the total particle velocity is non-applicable, are studied. The variational principles of the drift motion are extended to the case of the strong electric field. The generalized Littlejohn’s Lagrangian is obtained and the extended set of drift equations is derived. The possibility of particle acceleration due to the drift motion along the strong electric field is demonstrated.

On the Transition Between the Inner and Outer Plasma Sheet in the Earth's Magnetotail

AbstractWe have statistically studied the average structure and properties of the plasma sheet in the Earth's magnetotail at radial distances between R∼8 and 32 RE on the basis of ion, electron, and magnetic field data from the Geotail spacecraft. Here we discuss the transition between the inner plasma sheet and the outer plasma sheet near the equatorial plane. The ion and electron number densities, pressures, and energy fluxes at high energies, as well as the magnetic field, generally decrease with increasing radial distance from the Earth. The characteristics of the flux changes are reflected in the radial pressure gradients. If the transition between the inner and outer plasma sheet is determined by the radial pressure gradient change, the ion and electron transitions are located, on average, at R∼11 to 13 RE and R∼11 to 17 RE, respectively, at the midnight meridian. It is possible that the ion transition is located earthward of the electron transition. Furthermore, we have estimated the electric field, the electric and diamagnetic drift velocities, and the κ parameter (the square root of the ratio of the minimum curvature radius of the magnetic field line to the maximum gyroradius), which differ between the ion inner and outer plasma sheet.

Comment on “Ion velocity analysis of rotating structures in a magnetic linear plasma device” [Phys. Plasmas 25, 061203 (2018)

In a recent paper [Phys. Plasmas 25, 061203 (2018)], the authors have presented the analysis of the electric ion drift velocity experienced by heavy ions created in a plasma submitted to a low magnetic field. Unfortunately, they have used the classical E × B drift formula that is valid only in slab geometry. The authors have not taken into account that the cylindrical geometry induces a slow electric drift of the ions around the axis of the column. Moreover, the low magnetization of the ions induces a Larmor radius that is larger than the diameter of the plasma column. The movement of the ions immediately after their creation is parallel to the local electric field, not perpendicular as indicated by the authors. Most often, the ions are neutralized before experiencing the electric drift calculated along the classical guiding center theory. This has not been taken into account carefully by the authors so that the theoretical analysis of the Laser Induced Fluorescence measurements presented in this paper is clearly invalid.

Counter-Doped Multizone Junction Termination Extension Structures in Vertical GaN Diodes

GaN is an attractive wide bandgap semiconductor for power applications, owing to its superior electrical properties, such as high critical electric field and saturation drift velocity. Recent advancements in developing native GaN substrates has drawn attention toward exploring vertical GaN power diodes with high breakdown voltages (VBR). In practice, effective edge terminations techniques, such as junction termination extension (JTE) structures, play a crucial role in realizing high-voltage devices. Though certain challenges in fabricating GaN diodes, such as difficulty in forming p-type region, makes it difficult to realize edge termination, hence impeding the development and adoption of such devices. This paper aims to address these challenges by presenting the design and methodology of forming multi-zone, counter-doped JTE structures in vertical GaN diodes, which attains close to theoretical breakdown voltage for a wide range of tolerance in implant dose variation. Extensive device simulations using experimental data and including the effects of surface charges and implant profiles, are performed to present realistic results. The results suggest that >80% of ideal VBR is achievable for a wide range of doping concentration ( $2.4\times 10^{17}$ cm $^{-3}$ ) with a maximum VBR reaching 96% of the ideal value. This paper serves as the first step toward leveraging the current challenges in the fabrication of GaN diodes, by proposing optimum design techniques for realizing vertical GaN diodes with high breakdown voltages.

Three-dimensional magnetic reconnection in a collapsing coronal loop system

Context. Magnetic reconnection is believed to be the primary mechanism by which non-potential energy stored in coronal magnetic fields is rapidly released during solar eruptive events. Unfortunately, owing to the small spatial scales on which reconnection is thought to occur, it is not directly observable in the solar corona. However, larger scale processes, such as associated inflow and outflow, and signatures of accelerated particles have been put forward as evidence of reconnection. Aims. Using a combination of observations we explore the origin of a persistent Type I radio source that accompanies a coronal X-shaped structure during its passage across the disk. Of particular interest is the time range around a partial collapse of the structure that is associated with inflow, outflow, and signatures of particle acceleration. Methods. Imaging radio observations from the Nançay Radioheliograph were used to localise the radio source. Solar Dynamics Observatory (SDO) AIA extreme ultraviolet (EUV) observations from the same time period were analysed, looking for evidence of inflows and outflows. Further mpole magnetic reconstructions using SDO HMI observations allowed the magnetic connectivity associated with the radio source to be determined. Results. The Type I radio source was well aligned with a magnetic separator identified in the extrapolations. During the partial collapse, gradual (1 km s−1) and fast (5 km s−1) inflow phases and fast (30 km s−1) and rapid (80–100 km s−1) outflow phases were observed, resulting in an estimated reconnection rate of ∼0.06. The radio source brightening and dimming was found to be co-temporal with increased soft X-ray emission observed in both Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) and Geostationary Operational Environmental Satellite (GOES). Conclusions. We interpret the brightening and dimming of the radio emission as evidence for accelerated electrons in the reconnection region responding to a gradual fall and rapid rise in electric drift velocity, in response to the inflowing and outflowing field lines. These results present a comprehensive example of 3D null-point reconnection.

Intermittent electron density and temperature fluctuations and associated fluxes in the Alcator C-Mod scrape-off layer

The Alcator C-Mod mirror Langmuir probe system has been used to sample data time series of fluctuating plasma parameters in the outboard mid-plane far scrape-off layer. We present a statistical analysis of one second long time series of electron density, temperature, radial electric drift velocity and the corresponding particle and electron heat fluxes. These are sampled during stationary plasma conditions in an ohmically heated, lower single null diverted discharge. The electron density and temperature are strongly correlated and feature fluctuation statistics similar to the ion saturation current. Both electron density and temperature time series are dominated by intermittent, large-amplitude burst with an exponential distribution of both burst amplitudes and waiting times between them. The characteristic time scale of the large-amplitude bursts is approximately 15 . Large-amplitude velocity fluctuations feature a slightly faster characteristic time scale and appear at a faster rate than electron density and temperature fluctuations. Describing these time series as a superposition of uncorrelated exponential pulses, we find that probability distribution functions, power spectral densities as well as auto-correlation functions of the data time series agree well with predictions from the stochastic model. The electron particle and heat fluxes present large-amplitude fluctuations. For this low-density plasma, the radial electron heat flux is dominated by convection, that is, correlations of fluctuations in the electron density and radial velocity. Hot and dense blobs contribute only a minute fraction of the total fluctuation driven heat flux.

Negative Differential Resistance Observation and a New Fitting Model for Electron Drift Velocity in GaN-Based Heterostructures

The aim of this paper is an investigation of electric field-dependent drift velocity characteristics for Al0.3Ga0.7N/AlN/GaN heterostructures without and with in situ Si3N4 passivation. The nanosecond-pulsed current–voltage ( ${I}$ – ${V}$ ) measurements were performed using a 20-ns applied pulse. Electron drift velocity depending on the electric field was obtained from the ${I}$ – ${V}$ measurements. These measurements show that a reduction in peak electron velocity from $\text {2.01} \times \text {10}^{\text {7}}$ to $\text {1.39} \times \text {10}^{\text {7}}$ cm/s after in situ Si3N4 passivation. Also, negative differential resistance regime was observed which begins at lower fields with the implementation of in situ Si3N4 passivation. In our samples, the electric field dependence of drift velocity was measured over 400 kV/cm due to smaller sample lengths. Then, a well-known fitting model was fitted to our experimental results. This fitting model was improved in order to provide an adequate description of the field dependence of drift velocity. It gives reasonable agreement with the experimental drift velocity data up to 475 kV/cm of the electric field and could be used in the device simulators.

Particle acceleration in three-dimensional reconnection of flux-tube disconnection

“Flux-tube disconnection” is a type of steady-state three-dimensional magnetic reconnection with O-point at the origin of the resistive diffusion region. Magnetic reconnection is accepted as a potential mechanism for particle acceleration in astrophysical and space plasmas, especially in solar flares. By using the static magnetic and electric fields for flux-tube disconnection, features of test particle acceleration with input parameters for the solar corona are investigated. We show that a proton injected close to origin of the diffusion region can be accelerated to a very high kinetic energy along the magnetic field lines. The efficient acceleration takes place at the radial point where the electric drift velocity has its maximum magnitude. However, a proton injected at radial distances far away from the origin is not accelerated efficiently and even may be trapped in the field lines. The final kinetic energy of the particle depends significantly on the amplitude of the electric field rather than the amplitude of magnetic field.

Scrape-off layer turbulence in TCV: evidence in support of stochastic modelling

Intermittent fluctuations in the TCV scrape-off layer have been investigated by analysing long Langmuir probe data time series under stationary conditions, allowing calculation of fluctuation statistics with high accuracy. The ion saturation current signal is dominated by the frequent occurrence of large-amplitude bursts attributed to filament structures moving through the scrape-off layer. The average burst shape is well described by a double-exponential wave-form with constant duration, while the waiting times and peak amplitudes of the bursts both have an exponential distribution. Associated with bursts in the ion saturation current is a dipole-shaped floating potential structure and radially outwards directed electric drift velocity and particle flux, with average peak values increasing with the saturation current burst amplitude. The floating potential fluctuations have a normal probability density function while the distributions for the ion saturation current and estimated radial velocity have exponential tails for large fluctuations. These findings are discussed in the light of prevailing theories for filament motion and a stochastic model for intermittent scrape-off layer plasma fluctuations.

Phase space structures in gyrokinetic simulations of fusion plasma turbulence

Gyrokinetic simulations of fusion plasmas give extensive information in 5D on turbulence and transport. This paper highlights a few of these challenging physics in global, flux driven simulations using experimental inputs from Tore Supra shot TS45511. The electrostatic gyrokinetic code GYSELA is used for these simulations. The 3D structure of avalanches indicates that these structures propagate radially at localised toroidal angles and then expand along the field line at sound speed to form the filaments. Analysing the poloidal mode structure of the potential fluctuations (at a given toroidal location), one finds that the low modes m = 0 and m = 1 exhibit a global structure; the magnitude of the m = 0 mode is much larger than that of the m = 1 mode. The shear layers of the corrugation structures are thus found to be dominated by the m = 0 contribution, that are comparable to that of the zonal flows. This global mode seems to localise the m = 2 mode but has little effect on the localisation of the higher mode numbers. However when analysing the pulsation of the latter modes one finds that all modes exhibit a similar phase velocity, comparable to the local zonal flow velocity. The consequent dispersion like relation between the modes pulsation and the mode numbers provides a means to measure the zonal flow. Temperature fluctuations and the turbulent heat flux are localised between the corrugation structures. Temperature fluctuations are found to exhibit two scales, small fluctuations that are localised by the corrugation shear layers, and appear to bounce back and forth radially, and large fluctuations, also readily observed on the flux, which are associated to the disruption of the corrugations. The radial ballistic velocity of both avalanche events if of the order of 0.5ρ∗c0 where ρ∗ = ρ0/a, a being the tokamak minor radius and ρ0 being the characteristic Larmor radius, ρ0 = c0/Ω0. c0 is the reference ion thermal velocity and Ω0 = qiB0/mi the reference ion Larmor frequency for the characteristic amplitude of the magnetic field B0, qi and mi being, respectively, the ion charge and mass. The electric drift velocity is also found to exhibit a poloidal pattern, with maximum amplitude of the fluctuations either in the top or in the bottom regions of the machine depending on the sign of the zonal flow shear. This effect is found to be correlated to the stopping capability of the corrugation structures. The neoclassical properties stemming from the trapped particle drifts lead to large distortion of the distribution function. As expected, these prevail at the outer part of the simulation region despite the large collisionality. The distribution function fluctuations appear to be aligned along the v∥ = const. lines at constant poloidal angle. A specific symmetry is observed regarding the interplay of turbulence with the trapped-passing region.

Non-corotating models for pulsar magnetospheres

We reconsider pulsar electrodynamics for an obliquely rotating pulsar, and propose a way of synthesizing the vacuum dipole model (VDM) and the rotating magnetosphere model (RMM). We first modify the VDM by assuming that the parallel component of the inductive electric field is screened by charges. We refer to the resulting model as the minimal model. We calculate the screening charge density in the minimal model and compare it with the (Goldreich-Julian) charge density in the RMM. We identify the plasma velocity in the minimal model as the electric drift velocity due to the perpendicular component of the inductive electric field. We define a class of synthesized models as a linear combination of a fraction $y$ times the minimal model and $1-y$ times the RMM. These models require a gap (with $E_\parallel\ne0$) between the corotating stellar surface and the non-corotating magnetosphere. We present illustrative plots of the charge density, of the location of nulls (where the charge density is zero) and of the three components of the plasma velocity as a function of the angles ($\theta,\psi$) relative to the rotation axis, for specific values of the obliquity $\alpha$ and the parameter $y$. We discuss the question "Can any pulsar magnetosphere be corotating?" critically, pointing out difficulties associated with setting up corotation in the polar cap region. We speculate that the corotating plasma may flow across the last closed field line from the closed-field region. We suggest that abrupt changes in the spin-down rate in some pulsars may be due to jumps between the RMM and the minimal model.

On plasma rotation induced by waves in tokamaks

The momentum conservation for resonant wave-particle interactions, now proven rigorously and for general settings, is applied to explain in simple terms how tokamak plasma is spun up by the wave momentum perpendicular to the dc magnetic field. The perpendicular momentum is passed through resonant particles to the dc field and, giving rise to the radial electric field, is accumulated as a Poynting flux; the bulk plasma is then accelerated up to the electric drift velocity proportional to that flux, independently of collisions. The presence of this collisionless acceleration mechanism permits varying the ratio of the average kinetic momentum absorbed by the resonant-particle and bulk distributions depending on the orientation of the wave vector. Both toroidal and poloidal forces are calculated, and a fluid model is presented that yields the plasma velocity at equilibrium.

Applications Aspects of the Diffusion of Slow Electrons in the Ionospheric Gases

The paper presents the results of precise of the calculations of the diffusion of slow electrons in ionospheric gases, such as, (Argon – Hydrogen mixture, pure Nitrogen and Argon – Helium – Nitrogen) in the presence of a uniform electric field and temperature 300 Kelvin. Such calculations lead to the value Townsend's energy coefficient (KT) as a function of E/P (electric field strength/gas pressure), electric field (E), electric drift velocity (Vd), momentum transfer collision frequency ( ), energy exchange collision frequency ( ) and characteristic energy (D/?). The following physical quantities are deduced as function s E/P: mean free path of the electrons at unit pressure, mean energy lost by an electron per collision, mean velocity of agitation and the collisional cross-section of the molecules. The results are presented graphically and in tabular form. This results appeared a good agreement with the experimental data.

Applications Aspects of the Diffusion of Slow Electrons in the Ionospheric Gases

The paper presents the results of precise of the calculations of the diffusion of slow electrons in ionospheric gases, such as, (Argon – Hydrogen mixture, pure Nitrogen and Argon – Helium – Nitrogen) in the presence of a uniform electric field and temperature 300 Kelvin. Such calculations lead to the value Townsend's energy coefficient (KT) as a function of E/P (electric field strength/gas pressure), electric field (E), electric drift velocity (Vd), momentum transfer collision frequency ( ), energy exchange collision frequency ( ) and characteristic energy (D/?). The following physical quantities are deduced as function s E/P: mean free path of the electrons at unit pressure, mean energy lost by an electron per collision, mean velocity of agitation and the collisional cross-section of the molecules. The results are presented graphically and in tabular form. This results appeared a good agreement with the experimental data.